Question

The number of social interactions of ten minutes or longer over a​ one-week period for a group of college students is given in the following frequency table.​ (These interactions excluded family and work​ situations.) Find the​ mean, median,​ mode, and midrange for these data.
Social interactions in a​ week: x
4
6
13
16
21
28
31
38
40
47

Number of college​ students: f
12
19
19
19
10
11
4
3
3
3

Answer 1

First compute totals:
- n = sum f = 103
- sum(xf) = 1730

Mean = (sum xf)/n = 1730/103 ≈ 16.80 (≈16.796)

Median: the (103+1)/2 = 52nd observation. Cumulative f: 12, 31, 50, 69,... so the 52nd value lies in the x = 16 group. Median = 16

Mode: highest frequency is 19, occurring at x = 6, 13, and 16. The data are tri‑modal: modes = 6, 13, 16

Midrange = (min + max)/2 = (4 + 47)/2 = 25.5

Answers:
- Mean ≈ 16.80
- Median = 16
- Mode = 6, 13, 16
- Midrange = 25.5